Algorithm  shows a pseudocode for TBB-step methods for general nonlinear unconstrained optimization problems.
As usual (cf., e.g., [1]}), unlike the quadratic case of Algorithm REF , safeguards are added for the steplength.
We also include the nonmonotone line search strategy from [2]} (see Line 2). Line 3 features a well-known condition of sufficient decrease, where we take the common values of the line search parameters \(c_{\rm {ls}} = 10^{-4}\) , \(\sigma _{\rm {ls}} = \frac{1}{2}\)  (cf. [3]}), and \(M = 10\)  in the experiments. Global convergence of Algorithm  is proven in [4]}. In particular, it is possible to show R-linear convergence of the algorithm for uniformly convex functions (cf. [5]}). One of the key ingredients of [4]} is the uniform bounds on the stepsize, i.e., \(\beta _{k}^{\rm {}}\in [\beta _{\min }, \beta _{\max }]\)  for all \(k\) . Since the TBB stepsize (REF ) with safeguard lies in this interval, convergence of the algorithm is guaranteed; still, the initial starting steplength in the nonmonotone line search is different, which might lead to a smaller number of backtracking steps.
